 ## Ratio And Proportion

Before solving Ratio and Proportion Word Problems, you must know what Ratio and Proportion is. Various competitive examinations contain Ratio and Proportion Questions based on Class 6 to 10 syllabuses. Here are going to provide, ratio and proportion mixture problems, ratio proportion and variation problems with solutions, ratio and proportion word problems worksheet and many other Ratio and Proportion Aptitude Questions. This page is not only useful for the students of class 6 to 10 but is also helpful for the individual who are preparing for any competitive or entrance exam. Shortcut tricks to solve ratio and proportion problems will help you in upcoming Bank PO and other exams.

If you want to appear for Bank, SSC, Railway and other competitive examinations, then you must know Ratio and Proportion Concepts. This page contains ratio and proportion problems for Bank PO, ratio and proportion problems for class 6, ratio and proportion problems for class 7, ratio and proportion problems and solutions for class 9, ratio and proportion problems for class 8 and others.  Also, this page contains ratio and proportion problems and solutions pdf and how to solve ratio and proportion math problems, so must check it. By this Ratio and Proportion Online Test, you can have good command on Ratio and Proportion Word Problems. Go through this page that is designed by the team of www.privatejobshub.in, to get complete information related to ratio and proportion word problems with solutions.

### Ratio And Proportion Formula

Below Ratio And Proportion Basics Concepts are given. All the questions of Ratio And Proportion are solved with the help of these Basics Concepts. You have to apply one or more concepts to solve Ratio And Proportion Sums in competitive examination or Class 6 to 10 Examination. These formulas will be used to solve all type of Ratio And Proportion Problems.

Ratio:
• The ratio of two quantities p and q is defined as the fraction and we write it as p: q.
• In the ratio p : q, we call p as the first term or antecedent and q, the second term or consequent.
Eg. The ratio 3 : 4 represents 3/4 with antecedent = 5, consequent = 9.

Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.

Eg. 3 : 4 = 9 : 12 = 12: 16 Also, 6 : 3 = 2 : 1.
Proportion:
• The equality of two ratios is called proportion.
• If p : r = r : s, we write p : q :: r : s and we say that p, q, r, s are in proportion.
• Here p and s are called extremes, while q and r are called mean terms.  Ratio And Proportion PDF:

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Ratio and Proportion Methods Shortcut Tricks

To appear in any competitive or entrance exam is very important to know Ratio and Proportion shortcut tricks. To crack competitive exam you just need to know how to do time management. Time can managed in exams if you know the short cut tricks. Contenders can go through Shortcut Tricks of Ratio and Proportion and start practicing Ratio and Proportion questions with Shortcut Tricks.  Anything we learn in our school days was basics and that is well enough for passing our school exams. Now the time has come to learn for our competitive exams. For this we need our basics but also we have to learn something new. That’s where shortcut tricks and formula are comes into action.

Ratio And Proportion Problems And Solution

You can know how to Solve Ratio and Proportion by going through ratio and proportion problems with solutions those are given below. Different concepts are used in these Ratio And Proportion Aptitude Questions. Some of the questions are based on Ratio And Proportion Basics and in some questions tricks are used. Let’s get started with ratio and proportion problems with answers:

Ratio And Proportion Questions and Answer

You can know How to Solve Ratio and Proportion by going through Ratio And Proportion Questions that are given below. Different concepts are used in these Ratio And Proportion Aptitude Questions. Some of the questions are based on Ratio And Proportion Basics and in some questions tricks are used.

1. A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?

A. Rs. 460
B. Rs. 484
C. Rs. 550
D. Rs. 664

Explanation:

(4/15) A = (2/5)B
A = (2/5 x 15/4) B
A = (3/2) B
A/B = 3/2
A : B = 3 : 2.

B's share = Rs. (1210 x 2/5) = Rs. 484.

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2. If 0.75 : x :: 5 : 8, then x is equal to:

A. 1.12
B. 1.2
C. 1.25
D. 1.30

Explanation:

(x x 5) = (0.75 x 8) x = (6/5) = 1.20

3. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

A. 2 : 5
B. 3 : 5
C. 4 : 5
D. 6 : 7

Explanation:

Let the third number be x.
Then, first number = 120% of x =  120x/100 = 6x/5
Second number = 150% of x = 150x/100 = 3x/2
Ratio of first two numbers =          (6x/5 : 3x/2) = 12x : 15x = 4 : 5.

4. The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

A. 8 : 9
B. 17 : 18
C. 21 : 22
D. Cannot be determined

Explanation:

Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
= (120 /100 x 7x) and (110/100 x 8x)
= 42x/5 and 44x/5
= The required ratio = (42x/5 : 44x/5) = 21 : 22

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5. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

A.       2 : 3 : 4
B.       6 : 7 : 8
C.       6 : 8 : 9
D.       None of these

6. If Rs. 782 be divided into three parts, proportional to  :  : , then the first part is:

A. Rs. 182
B. Rs. 190
C. Rs. 196
D. Rs. 204

Explanation:

Given ratio =1/2 : 2/3 : 3/4  = 6 : 8 : 9.
1st part = Rs. 782 x 6/23 = Rs. 204

Explanation:

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
= (140/100 x 5x), (150/100 x 7x) and (175/100 x 8x)
= 7x, 21x/ 2 and 14x.
The required ratio = 7x : 21x /2: 14x
= 14x : 21x : 28x
= 2 : 3 : 4.

7. In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:

A. 20 litres
B. 30 litres
C. 40 litres
D. 60 litres

Explanation:

Quantity of milk = (60 x 2/3 litres) = 40 litres.
Let Quantity of water in it = (60- 40) litres = 20 litres.
New ratio = 1 : 2
Explanation:
Let quantity of water to be added further be x litres.
Then, milk : water = 40/ (20 + x)
Now, 40/  (20 + x) =          12
20 + x 80
20 + x = 80
x = 60.
Quantity of water to be added = 60 litres.

8. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?

A. Rs. 500
B. Rs. 1500
C. Rs. 2000
D. None of these

Explanation:

Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
x = 1000.
B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.

9. The fourth proportional to 5, 8, 15 is:

A. 18
B. 24
C. 19
D. 20

Explanation:

Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 : 15 : x
5x = (8 x 15)
x = (8 x 15)/ 5 = 24.

10. Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?

A. Rs. 17,000
B. Rs. 20,000
C. Rs. 25,500
D. Rs. 38,000

Explanation:

Then,  (2x + 4000)/ (3x + 4000) = 40/ 57
= 57(2x + 4000) = 40(3x + 4000)
= 6x = 68,000
= 3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.

11. The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:

A. 20
B. 30
C. 48
D. 58

Explanation:

Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8 =(5 x 3/5) : (8 x  3/5) = 3 : 24/5
A : B : C = 2 : 3 :24/5 = 10 : 15 : 24
B = 98 x 15/49 = 30

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12. The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

A. 3 : 3 : 10
B. 10 : 11 : 20
C. 23 : 33 : 60
D. Cannot be determined

Explanation:

Let A = 2k, B = 3k and C = 5k.
A's new salary = 115/100 of 2k = 115/100 x 2k = 23k/10
B's new salary = 110/100 of 3k = 110/100 x 3k = 33k/10
C's new salary = 120/100of 5k = 120/100 x 5k = 6k
New ratio 23k/10: 33k/10 : 6k = 23 : 33 : 60

13. Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:

A. 27
B. 33
C. 49
D. 55

Explanation:

Let the numbers be 3x and 5x.
Then,  (3x – 9)/(5x – 9) = 12/23
23(3x - 9) = 12(5x - 9)
9x = 99
x = 11.
The smaller number = (3 x 11) = 33.

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14. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

A.2 : 5
B. 3 : 7
C. 5 : 3
D. 7 : 3

Explanation:

Let 40% of A = 2/3 B
Then,  40A/100 = 2B/3
2A/5 = 2B/3
A/ B = (2/3 x 5/2) = 5/3
A : B = 5 : 3.

15. In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1:2:3. If there is Rs. 30 in all, how many 5 p coins are there?

A. 50
B. 100
C. 150
D. 200

Explanation:

Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.
Then, sum of their values = Rs. 25x/100 + (10 x 2x)/ 100 + (5 x 3x)/ 100 = Rs. 60x /100
60x/100 = 30 x = (30 x 100)/ 60 = 50
Hence, the number of 5 p coins = (3 x 50) = 150.

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